not sure if there is a particular reason why you have to have page/subpage as you cannot specify the / character for your page url. What you could do is use the hyphen so you could have www.mysite.com/page-subpage1 and www.mysite.com/page-subpage2 if you wanted and this fullfilled your needs.

This feature isn't in the daily builds. That blog post only meant there is a new URL handler that will make implementing sub-level URLs for pages easier. This means that what you're after isn't quite possible at this point in time.